Ellipsometers have been used for a number of years in measurements of thin films. In particular, ellipsometers have been used in the measurement of oxide and other layers on semiconductors. Ellipsometers analyse the ellipticity induced by reflection from a surface, measuring two parameters. This technique enables much more precise measurements than are possible using reflectometry measurements, for example.
A simple ellipsometer includes a light source which produces a beam of light which passes through a polarizer, forming a beam of light which is plane—polarised or has another well-defined polarisation state. The light source may be a laser or LED for single wavelength measurements, or a white light source for spectroscopic measurements. The beam passes through a retarder (sometimes referred to as a compensator) before striking the surface of a sample. The reflected light passes through a second polarizer (usually called the analyser) and enters a light detector. The light detector is usually a photodiode or a photomultiplier. An ellipsometer with a single photodiode or photomultiplier detector is a single channel ellipsometer.
The retarder may rotate. Alternatively, a birefringence modulator may be used. This modulator is typically a photoelastic modulator which includes an element with a birefringence dependent on the strain applied to it. A periodic strain is applied by a piezoelectric transducer, so that the birefringence is modulated at a high frequency (angular frequency ω0) usually in a mechanical resonance mode. Retarders may also be liquid crystal polarising devices.
A single channel birefringence-modulator ellipsometer has a sensitivity which is typically 100 times more than that of a common rotating-component ellipsometer. The ellipsometer has one detector. It achieves its very high sensitivity by using coherent lock-in amplifier detection operating at ω0 and 2ω0. This puts the electronics into a low noise region and the coherent detection of the lock-in with both frequency and phase eliminates noise signals which are not coherent with the modulator. Further, the modulation element undergoes mechanical resonance without motion of the centre of mass, and this eliminates motion of the light beam on the detector which often causes residual stray signals in the rotating-component design.
The usual configuration for a birefringence-modulator ellipsometer is Source, P, M, Sample, A, Detector, where P, M, and A are respectively the Polariser, Modulator and Analyser (sometimes it is used with the modulator following the sample). In the usual configuration the Polariser and Analyser are oriented at 45° and the modulator is parallel or perpendicular to the s direction (the s direction being parallel to the surface of the sample and perpendicular to the plane of incidence). ThenI=I0rs2{1+ρ2+2ρ2 cos(Δ+δ)}  (1)
Here I0 is the incident intensity, I the intensity following the Analyser, rs the magnitude of the s amplitude reflectivity, ρ and Δ are the parameters of the reflected polarisation ellipse, ρ the magnitude and Δ the phase angle, δ the modulator phase shift which varies with time as δ=δ0 sin ω0t. The expression can be expanded to readI∝1+ρ2+2ρ cos Δ cos δ−2ρ sin Δ sin δI∝1+ρ2+2ρ cos Δ{J0(δ0)+2J2(δ0)cos 2ω0t+ . . . }−2ρ sin Δ{2J1(δ0)sin ω0t+2J3(δ0)sin 3ω0t+ . . . }  (2)
Here J0, J1, J2 . . . are integer Bessel Functions dependent on the amplitude of the modulator phase shift δ0 and the series sums continue to higher order. The three lowest frequency terms are:the dc component Idc∝1+ρ2 cos (ΔJ0(δ0))  (3)the ac component at angular frequency ω0 Iω0∝2ρ(ΔJ1(δ0))sin ω0t  (4)the ac component at angular frequency 2ω0 I2ω0∝2ρ cos (ΔJ1(δ0))cos 2ω0t  (5)
Lock-in amplifiers tuned to ω0 and 2ω0 output the amplitudes of the ω0 and 2ω0 signals. The ratios ac(ω0)/dc and ac(2ω0)/dc provide two expressions for ρ and Δ from which these two parameters may be obtained. The ratios simplify if δ0 is chosen so that J0(δ0)=0, when
      x    =                            ac          ⁡                      (                          2              ⁢                              ω                o                                      )                          /        dc            =                        2          ⁢          ρcos          ⁢                                          ⁢          Δ                          1          +                      ρ            2                                ,      y    =                            ac          ⁡                      (                          ω              o                        )                          /        dc            =                                    2            ⁢            ρsin            ⁢                                                  ⁢            Δ                                1            +                          ρ              2                                      .            
Ellipsometers may be used in an imaging mode, where a multichannel array detector such as a CCD is used. In this case a rotating modulator has been used and a set of CCD images are recorded at different orientations of the retarder, which can then be analysed to form images of x and y, or ρ and Δ, over the illuminated sample area.
It would be desirable to use the beneficial features of a birefringence modulator (high stability modulation and little or no motion of the centre of mass) in such an ellipsometer. The frame rate of multichannel CCD detectors is typically in the range 20 to 200 frames per second, while the modulation frequency ω0 of a typical birefringence modulator is around 50 kHz. It is not possible to follow the rapidly changing modulated signal using an otherwise suitable detector.
A multi-detector ellipsometer is described in U.S. Pat. No. 5,757,671. The detectors used are photodiodes, with the signals from all detectors being multiplexed to a single analog/digital converter. The signal is subsequently Fourier decomposed. The x and y signals are not measured at the same time. This method is not readily extendable to a large number of channels.
A multichannel or multi-detector spectroscopic ellipsometer based on a birefringence modulator is an example of another desirable instrument. Here multichannel detectors could measure all colours at the same time. A straight forward method to achieve this would consist of many single channels detectors each with their associated two lock-in amplifiers. Such an instrument would be very bulky. Multichannel CCD detectors are again too slow to follow the modulation signals.